What is the first derivative test for critical points?

Answer 1

If the first derivative of the equation is positive at that point, then the function is increasing. If it is negative, the function is decreasing.

If the first derivative of the equation is positive at that point, then the function is increasing. If it is negative, the function is decreasing.
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Answer 2

The first derivative test for critical points states that if a function ( f(x) ) has a critical point at ( x = c ):

  1. If ( f'(x) ) changes sign from negative to positive at ( x = c ), then ( f(c) ) is a local minimum.
  2. If ( f'(x) ) changes sign from positive to negative at ( x = c ), then ( f(c) ) is a local maximum.
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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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